The money that many millionaires have is never enough, according to the UBS Wealth Management Americas Investor Watch report, When is Enough…Enough?

The report, released Tuesday, says many millionaires feel trapped on a treadmill that they cannot get off of because they want to preserve their families’ lifestyles.

The survey of 2,215 U.S. investors with more than $1 million in net worth revealed that, while millionaires recognize their good fortune, they feel compelled to strive for more, spurred on by their own ambition and an ever-present fear of losing it all, says UBS.

Seventy-seven percent of the millionaires grew up middle class or below and worked their way up the socioeconomic ladder with the goal of becoming a millionaire.

Overall satisfaction with life rises as net worth increases, the survey reveals. However, 58 percent of millionaires report feeling increased expectations for their standard of living over the last 10 years, so they keep striving for more. Higher expectations cause stress for millionaires about their ability to maintain the life they've built, UBS says. Among working millionaires with children at home, 52 percent feel like they are stuck on a treadmill, unable to get off without sacrificing their family's lifestyle.

“The majority of millionaires say they have worked hard to earn their wealth and appreciate the lifestyle it affords them and their families. But enough never seems to be enough -- even the wealthiest continue on the treadmill to achieve a better life,” says Paula Polito, client strategy officer, UBS Wealth Management Americas.

Reaching the millionaire mark also comes at a cost, with 64 percent of millionaires saying they had to give up precious family time to achieve their dreams.